Theorem 3ancoma 588

Description: Commutation law for triple conjunction.

Assertion

Ref	Expression
3ancoma	|- ((ph /\ ps /\ ch) <-> (ps /\ ph /\ ch))

Proof of Theorem 3ancoma

Step	Hyp	Ref	Expression
1		ancom 333	. . 3 |- ((ph /\ ps) <-> (ps /\ ph))
2	1	anbi1i 368	. 2 |- (((ph /\ ps) /\ ch) <-> ((ps /\ ph) /\ ch))
3		df-3an 583	. 2 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
4		df-3an 583	. 2 |- ((ps /\ ph /\ ch) <-> ((ps /\ ph) /\ ch))
5	2, 3, 4	3bitr4 158	1 |- ((ph /\ ps /\ ch) <-> (ps /\ ph /\ ch))

Syntax hints:   <-> wb 127   /\ wa 196   /\ w3a 581

This theorem is referenced by:  3ancomb 589  3anrev 590

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-3an 583

metamath.org